I like to imagine that if any of the Bat-Kids are out in public, whether they be getting food, shopping, patrolling, just walkin' around, whatever, that if they see the Bat-Signal pop on it's an unspoken rule between the siblings that they have to throw on their costume and try and find/deal with the trouble before Bruce gets there. Just to annoy him.
Batman: "Commissioner Gordon! I got here as fast as I could.. What's the situation?"
Commissioner Gordon: "Oh, Batman, thank you for coming.. It's alright, though, it's already been taken care of by these fellows."
*Gestures to the side where there's a couple of muggers sitting tied up next to Nightwing(He has pink, glittery shopping bags hanging all over his arms), Red Hood(He's rummaging through the bags Nightwing is holding, trying to find the black nail polish he just bought to touch up his nails after the fight), Red Robin(He's sipping a cup of coffee that he accidentally stole because he ran out of the cafe so quickly that he forgot to pay), and Robin(He's chowing down on a kids' meal from Bat-Burger)*
There's a bunch of adhd advice out there that's like "people with adhd tend to work better under deadlines due to the anxiety so here are ways to artificially induce a stress response in order to get you to get work done" and it's like well what if I don't want to be stressed out all the time in order to function